Lower and Upper Bounds on the Secret Key Rate for {QKD} Protocols Using One-Way Classical Communication

Barbara Kraus and Nicolas Gisin and Renato Renner

We investigate a general class of quantum key distribution (QKD)
protocols using one-way classical communication. We show that full
security can be proven by considering only collective attacks. We
derive computable lower and upper bounds on the secret key rate of
those QKD protocol involving only entropies of two–qubit density
operators. As an illustration of our results, we determine new bounds
for the BB84, the six-state, and the B92 protocol. We show that in all
these cases the first classical processing that the legitimate
partners should apply consists in adding noise. This is precisely why
any entanglement based proof would generally fail here.